Of concern is the energy decay property of solutions to wave equations with time-dependent damping. A reasonable class of damping coefficients for the framework of weighted energy methods is proposed, which contains not only the model of “effective” damping \((1+t)^{-\beta }\) \((-1\le \beta <1)\), but also non-differentiable functions with a suitable behavior at \(t\rightarrow \infty \). As an application of the weighted energy estimate, global existence for the corresponding semilinear wave equation is discussed.

中文翻译：

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具有瞬态阻尼的半线性波动方程的加权能量法

值得关注的是具有瞬态阻尼的波动方程解的能量衰减特性。为加权能量方法的框架提出了一类合理的阻尼系数，它不仅包含“有效”阻尼模型\((1+t)^{-\beta }\) \((-1\le \ beta <1)\) ，而且也是在\(t\rightarrow \infty \)处具有合适行为的不可微函数。作为加权能量估计的应用，讨论了相应的半线性波动方程的全局存在性。